Victoria builds a dollhouse in the shape of a right prism, as show below

The equation y 4.9t 2 3.5t 2.4 relates the height y in meters to the elapsed time t in seconds for a ball thrown downward at 3.5

tamaranim1 [39]

Answer:

$t \approx 0.43\,s$

Step-by-step explanation:

The vertical displacement function is $y(t) = -4.9\cdot t^{2}-3.5\cdot t + 2.4$ , where $y(t)$ is measured in meters and $t$ in seconds. Ball hits the ground when $y(t) = 0$ . That is:

$-4.9\cdot t^{2}-3.5\cdot t + 2.4 = 0$

Whose roots can be found by using the General Formula for Second-Order Polynomials:

$t_{1,2} = \frac{3.5\pm \sqrt{(-3.5)^{2}-4\cdot (-4.9)\cdot (2.4)} }{2\cdot (-4.9)}$

Solutions of this polynomial are:

$t_{1} \approx 0.43\,s,t_{2} \approx -1.14\,s$

Only the first root is physically consistent.

3 0

2 years ago

Ester's choir wants to learn a new song for the school concert in 7 weeks. The song has 3,016 lines. The choir learns an equal n

Ghella [55]

Answer:

the answer you will get is 61.5

Step-by-step explanation:

First you calcuate the number of days in the learning process there will be which there will be 49 days since 7 days x 7 weeks = 49 days. Then, you divide 3,016 and 49 to get 61.5510204 and then you round that up to get 61.5 or is you want a whole number with no decimals 62

3 0

2 years ago

Read 2 more answers

Amy and two of her friends eat lunch at a restaurant. Their bill, including tax, comes to $27.63. They decide to split the bill

Art [367]

Answer:

Step-by-step explanation:

$27.63 / 2 = $13.82

$13.82 * 0.20 = $2.76

$13.82 + $2.76 = $16.58

6 0

2 years ago

Which algebraic expressions are polynomials? Check all that apply. x2y 2 – 4x3 + 12y – x2 – 16 3.9x3 – 4.1x2 + 7.3

Softa [21]

Polynomials are the expressions that contain two or more algebra terms - constants, variables and their powers of a particular variable. The simple example of a polynomial is $2x^{2} + 3x^{3} + 5x + 2$

In the given question,
<span>9x3 – 4.1x2 + 7.3 is the polynomial because it has different powers of same variable x and does not contain any other variable.</span>

4 0

2 years ago

Read 2 more answers

In △ABC, m∠A=15 °, a=10 , and b=11 . Find c to the nearest tenth.

pshichka [43]

Answer:

The answer is:

$\bold{c\approx 20.2\ units}$

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

$cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Putting all the values.

$cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units$

The answer is:

$\bold{c\approx 20.2\ units}$

4 0

2 years ago