Sunday, April 11, 2021

Ekuacione kuadratike të rendit të dytë

Të zgjidhet ekuacioni $\displaystyle {{2}^{2x}}+5\cdot {{2}^{x}}-6=0$

Zgjidhje

Nga vetitë e fuqive mund të shkruajmë $\displaystyle {{2}^{2x}}={{\left( {{2}^{x}} \right)}^{2}}$ . Do të kemi:

$\displaystyle {{\left( {{2}^{x}} \right)}^{2}}+5\cdot {{2}^{x}}-6=0$

Duke zëvëndësuar $\displaystyle {{2}^{x}}$ me t do të kemi:

$\displaystyle {{t}^{2}}+5\cdot t-6=0$

E kthyem ekuacionin në ekuacion të fuqisë së dytë me një ndryshore.

Zgjidhjet e ekuacionit janë $\displaystyle {{t}_{1}}=1$ dhe $\displaystyle {{t}_{2}}=-6$ .

Tek fuqitë është marrë me marrëveshje se 1 është i barabartë me një fuqi me eksponent zero me çfarëdo baze të ndryshme nga zero. Pra, $\displaystyle {{2}^{x}}={{2}^{0}}$ del $\displaystyle x=0$ .

Ekuacioni $\displaystyle {{2}^{x}}=-6$ nuk ka zgjidhje sepse $\displaystyle {{a}^{x}}>0$ për çdo x.

Përgjigje: Zgjidhje e ekuacionit eksponencial është bashkësia $\displaystyle A=\left\{ 0 \right\}$ .

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brave payments verification

query_vars)) { $id = $wp->query_vars[BRAVE_WELL_KNOWN_URI_QUERY_VAR]; // run the more specific hook first do_action("well_known_uri_{$id}", $wp->query_vars); do_action("well-known-uri", $wp->query_vars); } } } add_filter('query_vars', array('BraveWellKnownUriPlugin', 'query_vars')); add_action('parse_request', array('BraveWellKnownUriPlugin', 'delegate_request'), 99); add_action('init', array('BraveWellKnownUriPlugin', 'add_rewrite_rules')); register_activation_hook(__FILE__, array('BraveWellKnownUriPlugin', 'activate_plugin')); register_deactivation_hook(__FILE__, 'flush_rewrite_rules'); function well_known_uri($query) { $options = get_option(BRAVE_WELL_KNOWN_URI_OPTION_NAME); if (is_array($options)) { foreach($options as $key => $value) { if (strpos($key, BRAVE_WELL_KNOWN_URI_MATCHER_SUFFIX) !== 0) continue; $offset = substr($key, strlen(BRAVE_WELL_KNOWN_URI_MATCHER_SUFFIX) - strlen($key)); $suffix = $options[BRAVE_WELL_KNOWN_URI_MATCHER_SUFFIX . $offset]; if ((empty($suffix)) || (strpos($query[BRAVE_WELL_KNOWN_URI_QUERY_VAR], $suffix) !== 0)) continue; $type = $options[BRAVE_WELL_KNOWN_URI_MATCHER_TYPE . $offset]; if (empty($type)) $type = 'text/plain; charset=' . get_option('blog_charset'); header('Content-Type: ' . $type, TRUE); $contents = $options[BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $offset]; if (is_string($contents)) echo($contents); exit; } } status_header(404); header('Content-Type: text/plain; charset=' . get_option('blog_charset'), TRUE); echo 'Not ' . (is_array($options) ? 'Found' : 'configured'); exit; } add_action('well-known-uri', 'well_known_uri'); // (mostly) adapted from Example #2 in https://codex.wordpress.org/Creating_Options_Pages class BraveWellKnownUriSettings { private $options; private $slug = 'well-known-admin'; private $option_group = 'well_known_option_group'; public function __construct() { add_action('admin_menu', array($this, 'add_plugin_page')); add_action('admin_notices', array($this, 'admin_notices')); add_action('admin_init', array($this, 'page_init')); } public function add_plugin_page() { add_options_page('Settings Admin', 'Brave Payments Verification', 'manage_options', $this->slug, array($this, 'create_admin_page')); } public function admin_notices() { settings_errors($this->option_group); } public function create_admin_page() { $this->options = get_option(BRAVE_WELL_KNOWN_URI_OPTION_NAME); ?>

Brave Payments Verification

option_group, BRAVE_WELL_KNOWN_URI_OPTION_NAME, array($this, 'sanitize_field')); $options = get_option(BRAVE_WELL_KNOWN_URI_OPTION_NAME); if (!is_array($options)) $j = 1; else { $newopts = array(); for ($i = 1, $j = 1;; $i++) { if (!isset($options[BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $i])) break; if (empty($options[BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $i])) continue; /* courtesy of https://stackoverflow.com/questions/619610/whats-the-most-efficient-test-of-whether-a-php-string-ends-with-another-string#2137556 */ $reversed_needle = strrev('_' . $i); foreach($options as $key => $value) { if (stripos(strrev($key), $reversed_needle) !== 0) continue; $newopts[substr($key, 0, 1 + strlen($key) - strlen($reversed_needle)) . $j] = $value; } $j++; } update_option(BRAVE_WELL_KNOWN_URI_OPTION_NAME, $newopts); for ($j = 1;; $j++) if (!isset($newopts[BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $j])) break; $j = 1; } for ($i = 1; $i <= $j; $i++) { add_settings_section($section_prefix . $i, 'Enter your Publisher Verification Code Below and click "Save Changes"', array($this, 'print_section_info'), $this->slug); add_settings_field(BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $i, $contents_title, array($this, 'field_callback'), $this->slug, $section_prefix . $i, array('id' => BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $i, 'type' => 'textarea')); } } public function print_section_info() {} public function field_callback($params) { $id = $params['id']; $type = $params['type']; $value = ''; $prefix = 'options[$id])) $value = esc_attr($this->options[$id]); $suffix = '" />'; } elseif ($type === 'textarea') { $prefix = ''; } echo($prefix . $value . $suffix); } public function sanitize_field($input) { $valid = array(); for ($i = 1;; $i++) { if (!isset($input[BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $i])) break; $valid += $this->sanitize_suffix($input, BRAVE_WELL_KNOWN_URI_MATCHER_SUFFIX . $i); $valid += $this->sanitize_type($input, BRAVE_WELL_KNOWN_URI_MATCHER_TYPE . $i); $valid += $this->sanitize_contents($input, BRAVE_WELL_KNOWN_URI_MATCHER_CONTENTS . $i); } return $valid; } public function sanitize_suffix($input, $id) { $valid = array(); if (empty($input[$id])) { $input[$id] = 'brave-payments-verification.txt'; $valid[$id] = $input[$id]; return $valid; } if (!isset($input[$id])) return $valid; $result = trim(sanitize_text_field($input[$id]), '/'); if (strstr($result, '/') !== FALSE) { add_settings_error($id, 'invalid_suffix', __('URI path must not contain "/"') . ' - ' . $result, 'error'); return $valid; } $valid[$id] = $result; return $valid; } // a 90% implementation of https://www.w3.org/Protocols/rfc1341/4_Content-Type.html // no self-respecting browser should have problems with a Content-Type header that this considers valid... public function sanitize_type($input, $id) { $valid = array(); $validP = TRUE; if (empty($input[$id])) { $input[$id] = 'text/plain'; $valid[$id] = $input[$id]; return $valid; } $parts = explode(';', $input[$id]); list($type, $subtype) = explode('/', $parts[0]); $token = '/^([0-9A-Za-z' . "'" . preg_quote('!#$%&*+^_`{|}~-') . '])+$/'; $word = '/^([0-9A-Za-z' . preg_quote('!#$%&*+^_`{|}~-') . '])+$/'; $string = '/^"([0-9A-Za-z' . preg_quote('!#$%&*+^_`{|}~-') . ']|(\\"))+"$/'; $type = trim(strtolower(sanitize_text_field($type))); if (empty($type)) { add_settings_error($id, 'missing_mime_type', __('Content-Type missing type'), 'error'); $validP = FALSE; } // skipping "media" types (audio, image, video) if ( (!in_array($type, array('application', 'message', 'multipart', 'text'))) && ((strpos($type, 'x-') !== 0) || (!preg_match($token, $type)))) { add_settings_error($id, 'invalid_mime_type', __('Content-Type has invalid MIME type') . ' - ' . $type, 'error'); $validP = FALSE; } $subtype = trim(sanitize_text_field($subtype)); if (empty($subtype)) { add_settings_error($id, 'missing_mime_subtype', __('Content-Type missing subtype'), 'error'); $validP = FALSE; } if (!preg_match($token, $subtype)) { add_settings_error($id, 'invalid_mime_subtype', __('Content-Type invalid subtype') . ' - ' . $subtype, 'error'); $validP = FALSE; } if (!$validP) return $valid; $result = $type . '/' . $subtype; for ($i = 1; $i < count($parts); $i++) { list($attribute, $value) = explode('=', $parts[$i]); $attribute = trim(sanitize_text_field($attribute)); if (empty($attribute)) { add_settings_error($id, 'missing_attribute', __('Content-Type missing attribute'), 'error'); $validP = FALSE; continue; } if (!preg_match($token, $attribute)) { add_settings_error($id, 'invalid_mime_attribute', __('Content-Type invalid attribute') . ' - ' . $attribute, 'error'); $validP = FALSE; } $value = trim(sanitize_text_field($value)); if (empty($value)) { add_settings_error($id, 'missing_value', __('Content-Type missing value'), 'error'); $validP = FALSE; } if (!(preg_match($word, $value) || preg_match($string, $value))) { add_settings_error($id, 'invalid_mime_value', __('Content-Type invalid value') . ' - ' . $value, 'error'); $validP = FALSE; } $result .= '; ' . $attribute . '=' . $value; } if ($validP) $valid[$id] = $result; return $valid; } public function sanitize_contents($input, $id) { $valid = array(); // nothing to sanitize, it's just raw text if (isset($input[$id])) $valid[$id] = $input[$id]; return $valid; } } if (is_admin()) new BraveWellKnownUriSettings(); ?>

Detyra të zgjidhura nga matematika

brave

Sunday, April 11, 2021

Ekuacione kuadratike të rendit të dytë

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