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2 years ago

The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers

Mathematics

1 answer:

e-lub [12.9K]2 years ago

7 0

Answer:

The numbers are 19 and 71.

Step-by-step explanation:

Let x and y represent the two numbers. Then x + y = 90.

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations. Since we already have the result of solution for y (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76. Thus, x = 76/4, or 19. If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.

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Given two vectors a⃗ =4.00i^+7.00j^ and b⃗ =5.00i^−2.00j^ , find the vector product a⃗ ×b⃗ (expressed in unit vectors). what is

FinnZ [79.3K]

The vector product of $\boxed{a \times b = - 43\hat k}$ and the magnitude of $a \times b$ is $\boxed{43}.$

Further explanation:

Given:

Vector a is $\vec a = 4.00\hat i + 7.00\hat j.$

Vector b is $\vec b = 5.00\hat i - 2.00\hat j.$

Explanation:

The cross product of a \times b can be obtained as follows,

$\begin{aligned}a \times b &= \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k} \\4&7&0\\5&{ - 2}&0 \end{array}}\right|\\&= \hat i\left( {0 - 0} \right) - \hat j\left( {0 - 0} \right) + \hat k\left( { - 9 - 35} \right)\\&= 0\hat i - 0\hat j - 43\hat k\\&= - 43\hat k\\\end{aligned}$

The vector can be expressed as follows,

$a \times b = - 43\hat k$

The magnitude of $a \times b$ can be obtained as follows,

$\begin{aligned}\left| {a \times b} \right| &= \sqrt {{0^2} + {0^2} + {{\left( { - 43} \right)}^2}}\\&= \sqrt {{{43}^2}}\\&= 43\\\end{aligned}$ 43404

The vector product of $\boxed{a \times b = - 43\hat k}$ and the magnitude of $a \times b$ is $\boxed{43}.$

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445.
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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Vectors

Keywords: two vectors, vector product, expressed in unit vectors, magnitude, vector a, vector b, a=4.00i^+7.00j^, b=5.00i^-2.00j^, unit vectors, vector space.

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